It is shown how axiomatic specifications of Boolean Algebras with
extra functions as well as propositional extension of standard
propositional logic can be transformed and simplified using syntactic
methods, in particular quantifier elimination algorithms for
second--order predicate logic.

This enables us to exploit representation theorems and model theoretic
semantics for these algebras and logics in such a way that for special
instances of these systems, i.e. particular algebras and particular
logics the corresponding specializations on the semantic side can be
computed automatically.

Special cases of the results of this paper are the theorem proving
aspects of J{\'o}nsson and Traski's representation theorem for Boolean
Algebras with operators, completeness of different possible worlds
semantics for modal logics and a clarification of the correlation
between correspondence and completeness in modal logics.

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MPG Unit:

Max-Planck-Institut für Informatik

MPG Subunit:

Programming Logics Group

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